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Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management

Author

Listed:
  • Tomasz Bielecki
  • Daniel Hernández-Hernández
  • Stanley R. Pliska

Abstract

In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only finite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then applied to the financial problem of managing a portfolio of assets which are affected by Markovian microeconomic and macroeconomic factors and where the investor seeks to maximize the portfolio's risk adjusted growth rate. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Tomasz Bielecki & Daniel Hernández-Hernández & Stanley R. Pliska, 1999. "Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 167-188, October.
    • Handle: RePEc:spr:mathme:v:50:y:1999:i:2:p:167-188
    DOI: 10.1007/s001860050094
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    Citations

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    Cited by:

    1. Anna Ja'skiewicz, 2007. "Average optimality for risk-sensitive control with general state space," Papers 0704.0394, arXiv.org.
    2. Çanakoglu, Ethem & Özekici, Süleyman, 2010. "Portfolio selection in stochastic markets with HARA utility functions," European Journal of Operational Research, Elsevier, vol. 201(2), pages 520-536, March.
    3. V. S. Borkar, 2002. "Q-Learning for Risk-Sensitive Control," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 294-311, May.
    4. Rolando Cavazos-Cadena & Mario Cantú-Sifuentes & Imelda Cerda-Delgado, 2021. "Nash equilibria in a class of Markov stopping games with total reward criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 319-340, October.
    5. Celikyurt, U. & Ozekici, S., 2007. "Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach," European Journal of Operational Research, Elsevier, vol. 179(1), pages 186-202, May.
    6. Daniel Hernández Hernández & Diego Hernández Bustos, 2017. "Local Poisson Equations Associated with Discrete-Time Markov Control Processes," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 1-29, April.
    7. U. Çakmak & S. Özekici, 2006. "Portfolio optimization in stochastic markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 151-168, February.
    8. Cui, Xiangyu & Gao, Jianjun & Shi, Yun & Zhu, Shushang, 2019. "Time-consistent and self-coordination strategies for multi-period mean-Conditional Value-at-Risk portfolio selection," European Journal of Operational Research, Elsevier, vol. 276(2), pages 781-789.
    9. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
    10. Grzegorz Andruszkiewicz & Mark H. A. Davis & S'ebastien Lleo, 2014. "Risk-sensitive investment in a finite-factor model," Papers 1407.5278, arXiv.org, revised Jan 2016.
    11. Ethem Çanakoğlu & Süleyman Özekici, 2009. "Portfolio selection in stochastic markets with exponential utility functions," Annals of Operations Research, Springer, vol. 166(1), pages 281-297, February.
    12. Shangzhen Luo & Xudong Zeng, 2014. "An optimal investment model with Markov-driven volatilities," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1651-1661, September.
    13. Özlem Çavuş & Andrzej Ruszczyński, 2014. "Computational Methods for Risk-Averse Undiscounted Transient Markov Models," Operations Research, INFORMS, vol. 62(2), pages 401-417, April.
    14. Xikui Wang & Yanqing Yi, 2009. "An optimal investment and consumption model with stochastic returns," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 45-55, January.
    15. Rolando Cavazos-Cadena & Raúl Montes-de-Oca, 2003. "The Value Iteration Algorithm in Risk-Sensitive Average Markov Decision Chains with Finite State Space," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 752-776, November.

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